Advanced gravitational wave detectors, such as Advanced LIGO [1]}, Advanced Virgo [2]}, and KAGRA [3]}, are designed to be quantum noise limited over most of their sensitivity spectrum. During their third observation period, the phase quadrature squeezed vacuum was successfully utilized in LIGO and Virgo, enabled a 3 \(\mathrm {dB}\)  quantum noise reduction above sub-100 Hz [4]}, [5]}. However, at the same time, the low frequency quantum noise originating from amplitude quadrature vacuum fluctuation was increased due to the Heisenberg uncertainty principle and approached the limit of the low frequency noise budget [6]}, [7]}, [8]}.
Thus, a broadband quantum noise reduction becomes indispensable for further sensitivity improvement, and requires the use of frequency dependent squeezed vacuum [9]}. Squeezed vacuum can obtain frequency dependence by reflection from a detuned optical cavity, called filter cavity. For advanced gravitational wave detectors operating with tuned signal-recycling cavity, one filter cavity having hundred Hertz linewidth and half-linewidth detuned is optimal [10]}, [11]}, [12]}, [13]}. Below 100 Hz, phase quadrature squeezed vacuum will be rotated to the amplitude quadrature, while high frequency squeezed vacuum is unchanged. Frequency dependent squeezed vacuum sources were developed in prototype [14]}, [15]} and will be used for the upcoming observation runs of Advanced Virgo+ [16]}, aLIGO+ [17]} and KAGRA [18]}. To operate an optical cavity, the laser frequency fluctuation and/or cavity mirrors' differential motion need to be controlled so that the cavity prompt reflected light can have a fixed phase difference with the light that enters, circulates and is leaked back from the cavity. When this phase difference is kept to be \(\pi \) , we say that the cavity is locked on resonance. But when this phase difference is held at an offset from \(\pi \) , we say that the cavity is locked with a detuning. In our experiment, the filter cavity length stability necessary for frequency dependent squeezing is achieved using an on-resonant 532 nm (green) beam, which is a harmonic of the 1064 nm (infrared) squeezed vacuum wavelength. The technique of controlling a laser beam's frequency using its own harmonic is referred to in this paper as bichromatic length control, and has been used for filter cavities [19]}, [14]}, optical parametric oscillators (OPOs) [21]}, [22]}, and arm length stabilization of gravitational wave detectors [23]}. However, initially, using bichromatic length control yielded a filter cavity detuning stability of the order of 30 Hz [14]} while the final goal is to achieve 1 Hz stability [25]}.
